Online Simplify Calculator
Reduce fractions to their lowest terms using GCD, or simplify square roots by extracting perfect squares.
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How Simplification Works
The fundamental concepts behind reducing mathematical expressions.
Fractions & GCD
To reduce a fraction, we must find the Greatest Common Divisor (GCD). This is the largest single number that divides evenly into both the numerator and denominator.
Example: 24 / 36
- Find GCD of 24 and 36, which is 12.
- Divide Top: 24 ÷ 12 = 2
- Divide Bottom: 36 ÷ 12 = 3
- Result: 2 / 3
Radicals & Perfect Squares
Simplifying a square root involves pulling out Perfect Squares (4, 9, 16, 25...). We factor the number inside the root into a perfect square and a non-perfect square.
Example: √72
- Find largest square factor of 72, which is 36.
- Rewrite: √(36 × 2)
- Split: √36 × √2
- Result: 6√2
Frequently Asked Questions
What does it mean to simplify a fraction?
Simplifying (or reducing) a fraction means making it as simple as possible. We do this by dividing both the top number (numerator) and bottom number (denominator) by the largest number that goes exactly into both of them (the Greatest Common Divisor, or GCD).
Why simplify fractions?
Simplified fractions are easier to understand, compare, and use in further calculations. For instance, it is much easier to picture "1/2" than "50/100", even though they represent the same amount.
How do you simplify a square root (radical)?
To simplify a square root, find the largest perfect square (numbers like 4, 9, 16, 25, etc.) that divides evenly into the number under the root. You can rewrite the root as a product of the perfect square and the remaining factor, then pull out the square root of the perfect square.
Can all square roots be simplified?
No. If a number has no perfect square factors greater than 1, its square root cannot be simplified further. For example, √15 cannot be simplified because its factors (3 and 5) are not perfect squares.
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